Estimating Regression Models Research Articles

Economic Impact of Droughts in Southern Brazil, a Duration Analysis

Hydrometeorological hazards are currently a cause for great concern worldwide. Droughts are among the most recurrent events, causing significant losses. This article presents a study on the duration of droughts in the southernmost state of Brazil, which has a large agricultural sector and experiences frequent drought events. The approach focuses on the economic recovery time of municipalities affected by the drought in 2020, 2022 and 2023, using the total value of invoices issued within each municipality between companies and from companies to consumers. The Kaplan–Meier estimator and Cox regression models are applied, incorporating covariates such as the size of the municipality, geographic location, and primary economic activity sector. The results show that the longest recovery period is concentrated in small cities, particularly in those where agriculture or livestock is the primary economic activity. The greatest resilience is observed in cities within the metropolitan region, where economic activity is more concentrated in services and industry and where populations are generally larger. The study identifies that after each drought event, at least 75% of municipalities achieve economic recovery within 3 months. These findings support better planning for both drought prevention and impact reduction and they are relevant for the development of economic and social policies.

Abstract 4139198: A Systematic Approach to Prompting Large Language Models for Automated Feature Extraction from Cardiovascular Imaging Reports

Introduction: Cardiovascular radiology reports contain valuable diagnostic information linked to images, but the unstructured text format makes feature extraction difficult on a large scale. Large language models (LLMs) allow for feature extraction where string parsing alone is insufficient, but require careful prompting for accurate results. Hypothesis: We hypothesize that a systematic prompting approach using LLMs can expedite the extraction of features from unstructured text in transesophageal echocardiography (TEE) reports. Methods: The data consisted of 7106 intraoperative TEE reports, 600 of which were manually reviewed to obtain pre- and post-intervention ground truth values for left ventricular ejection fraction (LVEF), right ventricular systolic function (RVSF), and tricuspid regurgitation (TR). Reports are paired with an imaging study consisting of 50-200 clips. For each feature considered, 100 of the 600 labeled reports were used to engineer a prompt in Llama-2 that maximized feature extraction accuracy. Results: We found that using multiple, shorter prompts yielded higher accuracy than did fewer, longer prompts. Additionally, when imposing semantic information onto a numerical scale, prompt engineering in combination with string parsing (Figure 1) gave the best results. When evaluated on the 500 labeled reports withheld for testing, the finalized prompts had accuracies of 94.1%, 94.8%, and 91.3% for LVEF, RVSF, and TR, respectively. Using this strategy, 5000 intraoperative TEE reports were analyzed and used to train and evaluate a regression model for LVEF estimation from TEE clips (Figure 2). Conclusion: We have shown that performing prompt engineering on Llama-2 can be used to extract features from unstructured TEE reports in an accurate manner. As an extension of these methods, automated feature prediction from echocardiograms can be used to create rapid, low-cost, and accessible cardiac assessments.

On remedying the presence of heteroscedasticity in a multiple linear regression modelling

This study demonstrated the very essence of remedying the presence of heteroscedasticity, where it existed, in regression modelling. Two different hypothetical data, Data A (the Original) and Data B (the Original), were used in this study for the purpose of illustration. The normality, multicollinearity and autocorrelation assumptions were satisfied, but the Breusch-Pagan test and the White test established the existence of heteroscedasticity in the two datasets. The estimated multiple linear regression model for Data A (the Original) was statistically significant with an R-square value of 0.976, an AIC value of 332.5929, and an SBC value of 347.2533; and the one for Data B (the Original) was also statistically significant with an R-square value of 0.553, an AIC value of 69.89669, and an SBC value of 82.15499. The Log-transformation was applied on the variables in Data A (the Original) and Data B (the Original) to give rise to new sets of data, Data A (Now with Heteroscedasticity Remedied) and Data B (Now with Heteroscedasticity Remedied); which equally satisfied the normality, multicollinearity and autocorrelation assumptions, and also satisfied that there were no existence of heteroscedasticity in the two datasets. Now, the estimated multiple linear regression model for Data A (Now with Heteroscedasticity Remedied) was statistically significant with an R-square value of 0.986, an AIC value of -135.021, and an SBC value of -120.361; and the estimated model for Data B (Now with Heteroscedasticity Remedied) was statistically significant with an R-square value of 0.624, an AIC value of -32.0801, and an SBC value of -19.8218. From the points of view of the values of the R-square (0.986>0.976 and 0.624>0.553), AIC (-135.021<332.5929 and -32.0801<69.89669) and SBC (-120.361<347.2533 and -19.8218<82.15499), it was evident that the estimated regression models for Data A (Now with Heteroscedasticity Remedied) and Data B (Now with Heteroscedasticity Remedied) were, respectively, better models when compared to the regression models for Data A (the Original) and Data B (the Original).

Value Chain Analysis of Haricot Bean in East Shewa Zone, Oromia Regional State, Ethiopia

The key objectives of the study were identifying haricot bean value chain actors, their functions and relationship among them, examining actor’s performance along the chain and analyzing factors affecting supply to the market and factors affecting market outlet choice in the study area. Both primary and secondary sources were used for data collection. The primary data was collected through interviewing 180 sample household farmers and 40 traders using semi-structured questionnaires. STATA version 15 Software was used for data analyzing. As the descriptive result indicate that, on average farmers allocate 0.72ha of land for haricot bean production, from which 21.72qt/ha of output gained. In the value chain of haricot bean input suppliers, farmers, collectors, traders, transporters and consumers are the major value chain actors who perform various value chain. From the study result, six marketing channels of haricot bean are exhibited in the study areas. Estimates of the multiple linear regression models indicate that the level of haricot bean supplied to the market is determined by educational level of household, haricot bean farming experience, land allocated for haricot bean, market price of haricot bean, TLU, access to credit, and access to market information. Therefore, policy makers should focus more on the abovementioned variables in the future intervention to increase volume of haricot bean supplied to the market. As the multivariate probit model result indicated that the market outlet choice of rural assemblers was positively and significantly influenced by distance to the nearest market center, distance to all weather road, and educational level whereas it’s negatively and significantly influenced by output level where as selling direct to consumers outlet choice was negatively and significantly affected by sex of household, educational level, farm experience of household in haricot bean, and output level. Urban traders/wholesalers market outlet was positively and significantly affected by sex of household, educational level, haricot bean farm experience, access to credit, access to market information, membership of cooperative, and output level whereas it’s negatively influenced by distance to the nearest market center, distance to all weather road and extension service. Based on the findings of this study, some relevant implications can be drawn that can assist to design appropriate intervention mechanisms to improve market outlets choice of haricot bean farmers in the study area.

Comparison between estimates of beta regression model using MSE

The multiple linear regression analysis shows the effects of explanatory variables on the dependent variable. Its function is to represent data to understand the shape and nature of the relationship between explanatory variables and the response variable. One of the main problems faced by linear regression is the nature of the data, as sometimes it does not follow a normal distribution. This has led to the emergence of different types of linear regression models such as the beta regression model, where the data of the dependent variable is less than one and confined within the period (0,1), and the data is relative and decimal. Non-traditional methods will be used to estimate beta regression parameters because some traditional methods do not provide suitable and accurate results when dealing with one of the main problems encountered in regression, which is multicollinearity. To address this issue, we used some methods include The Maximum Likelihood Estimation (MLE), ridge regression, modified Liu, and Ozkale and Kaciranlar method. Shrinking parameters are proposed for each method, and a comparison between the methods is conducted using the Mean Squared Error comparison criterion through a simulation experiment with two approaches, the simulation results showed that the ridge regression method is the best for the first and second methods of simulation. Paper type Research Paper

Computed tomography study of cranial vault thickness in Malaysian subadult population.

Cranial vault thickness (CVT) and its variations provide valuable insights into an individual's biological attributes such as age and sex. This paper aimed to assess the correlations of CVT with age and sex and develop a regression model for age estimation in Malaysian subadults using computed tomography (CT) images. A total of 521 CT images (male/female: 279/242; age range: 0-20 years; Malay/Chinese/Indian: 221/145/155) were included in the study. Correlations of CVT measurements with age and sex, including frontal bone thickness (FBT), occipital bone thickness (OBT), left parietal bone thickness (LPBT), and right parietal bone thickness (RPBT) were assessed and regression formulae were developed for age estimation in subadults. A significant correlation between CVT measurements and age was demonstrated (p < 0.001). Age estimation was most accurate in the younger age group (< 2 years) at frontal and occipital, and accuracy decreases in the older age groups. Additionally, sexual dimorphism was evident in the frontal and parietal bone thickness within the age range of 3-6 years and 16-20 years, respectively. In conclusion, the findings suggested CVT measurements could be used to corroborate other age estimation methods for subadults.

Asymmetric Effects of Real Exchange Rate on Turkey's Imports: Threshold Value Regression Model

Determinants of imports are one of the most discussed topics in the foreign trade literature. This study explores the asymmetric relationship between the real exchange rate and imports for Turkey example. The paper employs monthly data spanning from 2013:01 to 2023:06, estimating classical least square estimation and Threshold Regression Models, subsequently comparing their outcomes. The findings highlighted that the relations between imports and real exchange rate are asymmetric. According to the least square estimation model, it was noted that the real exchange rate had a negative impact on imports, aligning with anticipated outcomes. In the threshold regression model, it was seen that movements in the real exchange rate positively affected imports in the model below the threshold, while exerting a negative effect in the model above the threshold. This finding was interpreted as increasing imports by buying the expectation that the exchange rate increases, which are below the internalizable level, may increase further. It is considered essential for policymakers to take into account asymmetric relationships when analyzing the relationships between imports and the exchange rate.

Influence of prior heart valve intervention on treatment and disease trajectory after diagnosis of heart failure with reduced ejection fraction

Abstract Background and aim Among patients with heart failure with reduced ejection fraction (HFrEF), knowledge is scarce on whether patients with prior valvular heart disease (VHD) intervention are distinct regarding clinical characteristics, treatment, and prognosis. Methods Using the Danish Heart Failure Registry and nationwide administrative registries, we identified patients with new-onset HFrEF from 2008 to 2021. Within this cohort, patients with a prior VHD intervention were identified and matched 1:5 on age-, sex-, in/outpatient presentation, and year of HFrEF diagnosis with remaining patients (controls). Outcomes were 1) baseline use and up-titration of guidelines-directed medical therapy (GDMT) and implementation of implantable cardioverter-defibrillator or cardiac resynchronization therapy with pacemaker/defibrillator (ICD/CRT-P/D) at 6 months follow-up, and 2) a composite of HF hospitalization or all-cause death at 3 years follow-up. The Kaplan-Meier estimator and Cox regression models, adjusted for HF severity, socioeconomic status, and major comorbidities, were used to compare the composite outcome, with patients without prior heart valve intervention as reference. Results The study cohort comprised 32,713 patients, of whom 1196 (3.6%) underwent a prior VHD intervention (median time since intervention 10 months). After matching, the study population were 1151 cases (median age 74 years, 82% men), and 3769 matched controls. Among cases and controls, median left ventricular ejection fraction was similar (30% vs. 30%) and the proportion in New York Heart Association (NYHA) class II was alike (82% vs 83%). At the time of HFrEF diagnosis, numerically more cases were on a beta-blocker (62% vs. 53%), ACEi/ARB/ARNI (48% vs. 44%), MRA (19% vs. 14%), and more had an implementation of (ICD/CRT-P/D) (17 % vs. 7%) (Figure 1). At 6 months, ≥ 50% of the daily target dose was achieved in (46% vs. 46%) for beta-blockers, (47% vs. 47%) for ACEi/ARBs/ARNI, (31% vs. 33%) for MRA, and implementation of ICD/CRT-P/D was attained in (28% vs. 18%), among cases and controls, respectively (Figure 1). The 3-year risk of HF hospitalization or all-cause death was 25% in cases and 24% in controls (Figure 2) with no significant differences (hazard ratio (HR) 0.95 , 95% confidence interval (CI) 0.84-1.08) compared to controls. Conclusions Patients with new-onset HFrEF and prior VHD interventions received more GDMT and had a higher implementation of ICD/CRT-P/D at the time of HFrEF diagnosis. However, following diagnosis, no major differences in GDMT initiation and up-titration, implementation of ICD/CRT-P/D, and the adjusted rates of HF hospitalization or all-cause death were observed among patients with and without prior heart valve intervention.Figure 1 Guideline-directed medicationFigure 2 Crude cumulative risk

Relapse of infective endocarditis after cardiac implantable electronic device removal compared to a conservative strategy

Abstract Background According to current guidelines, complete removal of cardiac implantable electronic device (CIED) should be considered in patients with valvular infective endocarditis (IE), accounting for the identified pathogen and need for valve surgery (Class IIa recommendation). Unselected longitudinal data are needed to assess this strategy. Purpose To examine IE readmission after IE discharge according to status of CIED removal in patients with conservatively treated IE. Methods Using Danish nationwide registries, we identified patients aged ≥18 years with first-time IE from 2010-2021. We included patients with conservatively treated IE and a CIED, who were alive at IE discharge. Patients who underwent CIED removal during IE admission were compared to those without removal, examining the study outcome of IE readmission within six months after IE discharge. An initial blanking period of 14 days was applied after IE discharge. The Aalen-Johanson estimator and multivariable Cox regression models were used to determine cumulative incidences and adjusted hazard ratios (HRs) of IE readmission according to status of CIED removal, respectively. Results Among 6,843 patients with first-time IE, 5,731 (83.7%) were conservatively treated. Of these, 1,201 (21.0%) had a CIED, of which 205 (17.1%) died during IE admission. Thus, the final study population comprised 996 patients alive at IE discharge. The median age of the study population was 75.5 years (interquartile range [IQR]: 67.9-82.0), and 753 (75.6%) were males. In total, 574 (57.6%) patients underwent CIED removal during IE admission. Patients who underwent CIED removal were younger, compared to patients without CIED removal, 73.1 years (IQR: 65.7-79.1) versus 79.0 years (IQR: 71.3-85.1), respectively. The six-month cumulative incidence of IE readmission was 2.0% (95% confidence interval [CI]: 1.1-3.5%) in patients who underwent CIED removal versus 6.1% (95% CI: 4.0-8.9%) in patients without CIED removal (P-value=0.001) (Figure 1). CIED removal was associated with a significantly lower six-month rate of IE readmission, compared to no CIED removal (HR: 0.36 [95% CI: 0.17-0.77]). Relapse bacteraemia (including IE) with the same microorganism as first-time IE occurred in 2.2% of patients who underwent CIED removal and in 5.4% of patients without CIED removal. Staphylococcus aureus was the most common microorganism in 33.3% of patients with relapse bacteraemia who underwent CIED removal. Conclusions In this nationwide study, the six-month rate of infective endocarditis (IE) readmission was three-fold lower in patients who underwent cardiac implantable electronic device (CIED) removal, compared to patients without CIED removal. The current findings suggest that CIED removal is associated with lower risk of relapse of IE in patients with conservatively treated IE. These results are in line with current guideline recommendations. However, more randomized clinical trial data are needed.

Selection of optimal spectral features for leaf chlorophyll content estimation

Leaf chlorophyll content (LCC) is crucial for monitoring the physiological processes of crops. Many studies have utilized spectral features to develop regression models for accurate LCC estimation, enabling the quantitative assessment and evaluation of crop growth status. The selection of optimal spectral features and regression algorithms significantly affects the precision of LCC estimation. In this study, we compared and analyzed the optimal spectral features for LCC estimation, as well as the consistency of machine learning methods across different crop types, phenology periods, and sensors. First, we extracted various spectral features, including the original spectral features (OS), first-order derivative spectral features (FDS), original continuum-removed spectra (CR) along with their four related derivative spectral features, principal component variables derived from different spectral features, and highly correlated spectral features with LCC. These extracted spectral features were then employed to construct the LCC models using six common regression algorithms on different datasets. Finally, we analyzed the optimal combination of spectral features and regression algorithms for accurate LCC estimation considering various dimensions, such as crop type, phenological period, and sensor used in observation conditions. The results demonstrate that the combinations of the principal component variables of continuum-removed derivative reflectance with the top 10 correlations with LCC (PCA_CRDR_R) combined with Gaussian process regression (GPR) can be considered as the optimal choice for estimating LCC under diverse observation conditions at a canopy scale, and its R2 can reach 0.62 for sugar beet LCC estimation; thus providing valuable theoretical guidance for selecting appropriate spectral features for LCC estimation.

Tax Evasion and Company Survival: A Brazilian Case Study

Enterprises face significant growth and survival challenges in highly competitive markets. Many companies fail to meet their tax obligations, which deprives society of essential resources and often results in tax penalties. This article examines whether companies that receive tax fines for evasion have a longer or shorter life expectancy compared to those that consistently comply with tax regulations. To analyze survival rates, the Kaplan–Meier estimator and Cox regression model were applied, considering factors such company size, sector, location, and tax evasion fines. The study included data from 11,297 firms established in 2017, in Rio Grande do Sul, Brazil. The findings indicate that companies fined for tax evasion had a higher survival rate (69%) compared to those without fines (38%) by 2023. This suggests that fines might serve as a corrective measure, helping companies realign and improve their chances of survival. Additionally, the study shows that medium-sized enterprises face significant challenges, possibly due to exceeding the limits of a simplified tax regime. This study highlights the importance of continued research across different regions and countries to validate these findings and enhance tax administration strategies.

Two-stage pseudo maximum likelihood estimation of semiparametric copula-based regression models for semi-competing risks data.

We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. With a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated using only the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated together via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness than the one-stage procedure developed in Chen YH (Lifetime Data Anal 18:36-57, 2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu H et al., (Commu Statistics-Theory Methods 51(22):7830-7845, 2021) . An R package PMLE4SCR is developed to implement our proposed method.

Bayesian stein-type shrinkage estimators in high-dimensional linear regression models

Bayesian stein-type shrinkage estimators in high-dimensional linear regression models

Modeling forest canopy structure and developing a stand health index using satellite remote sensing

Biotic and abiotic disturbances modify tree structure and degrade stand health. Accurate geospatial data on stand structure is important for monitoring tree growth, forest health, progression and severity of diseases and pests, and estimating resilience to climate stress. The live crown ratio (LCR) of trees serves as a key health indicator but has been understudied at the landscape level using remote sensing data. This study generated the leaf area index (LAI) and a novel spatial layer of LCR at site and landscape scales using a combination of satellite data and ground observations. We conducted field surveys to collect plot-level (10 m × 10 m) data in four eastern white pine (EWP; Pinus strobus L.)-dominated sites in the state of Maine, USA. The plot-level data were used to develop regression models for LAI and LCR estimation using microwave (Sentinel-1) and optical (Sentinel-2) remote sensing data and applying the Random Forest (RF) and Support Vector Machine (SVM) machine learning algorithms. The RF model showed higher prediction accuracy than the SVM model at the site level. Moreover, the prediction accuracy at the site and landscape levels were comparable for LAI (R2 > 0.76) and LCR (R2 > 0.71) using the RF model. Furthermore, the predicted LAI and LCR were integrated with canopy height and stand density to develop a novel health index map for EWP. The resulting health index map successfully delineated patches representing various health categories. Forestry practitioners and decision-makers can use the derived health index map and intermediate spatial data layers (LAI and LCR) to guide stand management. The developed framework can potentially be applied to other coniferous and broadleaved species for remote sensing-based LCR estimation and forest health assessment upon further studies and verification.

Quantile-based robust Kibria–Lukman estimator for linear regression model to combat multicollinearity and outliers: Real life applications using T20 cricket sports and anthropometric data

The performance of ordinary least squares (OLS) and ridge regression (RR) are influenced when outliers are present in y-direction with multicollinearity among independent variables. The robust RR with ridge parameters provides a biased estimator that has a smaller variance than conventional OLS and RR estimators. The optimal value of the ridge parameter has a vital role in bias-variance tradeoff. This study proposes quantile-based estimation of ridge parameter in robust RR to deal with the joint issue of y-direction outliers and multicollinearity. The effectiveness of the proposed estimators is evaluated using intensive Monte Carlo simulation and two real data sets in terms of mean square error (MSE) and predictions sum of squared error (PSSE) criterion. Simulation findings reveal that the newly developed estimators of ridge parameter in robust RR have better performance than OLS, RR, and existing robust RR estimators when errors are normally and non-normally distributed. The results from two numerical examples of T20 Cricket sports and anthropometric data show that the new estimator with quantile probability 0.50 and 0.99 respectively has winning performance among all competing and proposed estimators.

Prevalence of Depressive Symptoms in a Predominantly Hispanic/Latinx South Texas Community in the Aftermath of the COVID-19 Pandemic.

COVID-19 has a lasting impact on mental health, particularly within the Hispanic/Latinx communities. This paper empirically investigates the post-COVID-19 presence and severities of depression, one of the most common mental health disorders, among adults in a predominantly U.S.-born Hispanic/Latinx community in South Texas composed primarily of Mexican Americans. Multiple statistic regression models were applied to data from 515 adults in Nueces County who completed all questions in a survey from convenience sampling between June 2022 and May 2023. Depression was assessed using both standard PHQ-2 and PHQ-9 measurements. Of the 515 participants, 377 (64.5%) were Hispanic, and 441 (85.6%) had a high school education or higher, reflecting the county's demographics. About half of the participants (47%) reported mild/moderate to severe depression. The regression model estimation results reveal that female participants, those not in full-time employment, and individuals with disabilities were more likely to feel depressed after COVID-19. Middle-aged adults demonstrated greater resilience to depression compared to other age groups. Notably, non-Hispanic participants in the study reported higher levels of depression compared to their Hispanic counterparts. Additionally, COVID-19-related experiences, such as testing positive for the virus, being hospitalized, or having a history of depression before COVID-19, were associated with higher levels of reported depression. COVID-19 has significantly impacted the mental health of this predominantly U.S.-born Hispanic/Latinx community. These findings can assist healthcare providers and policymakers in developing targeted strategies to tailor interventions aimed at enhancing mental health well-being, reducing disparities, and fostering overall improvement within the Hispanic/Latinx community.

Robust multi-outcome regression with correlated covariate blocks using fused LAD-lasso

Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust fused LAD-lasso method for multiple outcomes is presented that addresses the challenges of non-normal outcome distributions and outlying observations. Measured covariate data from space or time, or spectral bands or genomic positions often have natural correlation structure arising from measuring distance between the covariates. The proposed multi-outcome approach includes handling of such covariate blocks by a group fusion penalty, which encourages similarity between neighboring regression coefficient vectors by penalizing their differences, for example, in sequential data situation. Properties of the proposed approach are illustrated by extensive simulations using BIC-type criteria for model selection. The method is also applied to a real-life skewed data on retirement behavior with longitudinal heteroscedastic explanatory variables.

Bayesian ridge estimators based on a vine copula-based prior in Poisson and negative binomial regression models

Poisson and negative binomial regressions are popular methods for modelling the relationship between a count variable and explanatory variables. In the presence of multicollinearity, ridge regression is an alternative to the maximum likelihood estimation for regression coefficients. Furthermore, ridge estimators are interpreted as the Bayesian posterior mean (or mode) when the regression coefficients follow a multivariate normal prior. However, using the multivariate normal prior may not effectively estimate regression coefficients, especially in the presence of interaction terms. This study proposes vine copula-based priors for Bayesian ridge estimators in Poisson and negative binomial regression models. The simulations and data analysis results indicate that for the Poisson model with equidispersion and the negative binomial model with overdispersion, the Clayton and Gumbel copula priors of the Archimedean family achieve superior performance than the multivariate normal prior and Gaussian copula prior.

Weighted fast-trimmed likelihood estimator for mixture regression models

The fast-trimmed likelihood estimate is a robust method to estimate the parameters of a mixture regression model. However, this method is vulnerable to the presence of bad leverage points, which are outliers in the direction of independent variables. To address this issue, we propose the weighted fast-trimmed likelihood estimate to mitigate the impact of leverage points. The proposed method applies the weights of the minimum covariance determinant to the rows suspected of containing leverage points. Notably, both real data and simulation studies were considered to determine the efficiency of the proposed method compared to the previous methods. The results reveal that the weighted fast-trimmed estimate method is more robust and reliable than the fast-trimmed likelihood estimate and the expectation–maximization (EM) methods, particularly in cases with small sample sizes.

A new robust approach for the polytomous logistic regression model based on Rényi's pseudodistances.

This paper presents a robust alternative to the maximum likelihood estimator (MLE) for the polytomous logistic regression model, known as the family of minimum Rènyi Pseudodistance (RP) estimators. The proposed minimum RP estimators are parametrized by a tuning parameter $\alpha \ge 0$, and include the MLE as a special case when $\alpha =0$. These estimators, along with a family of RP-based Wald-type tests, are shown to exhibit superior performance in the presence of misclassification errors. The paper includes an extensive simulation study and a real data example to illustrate the robustness of these proposed statistics.